Effects of endomorphisms on the commutativity of banach algebras

TL;DR

This paper investigates how endomorphisms influence the commutative properties of Banach algebras using topological and algebraic methods, highlighting the importance of specific assumptions through examples.

Contribution

It introduces new insights into the effects of endomorphisms on Banach algebra commutativity, emphasizing the role of certain assumptions with illustrative examples.

Findings

Endomorphisms can alter the commutativity of Banach algebras.

Certain assumptions are necessary for preserving commutativity.

Topological and algebraic techniques are effective in this analysis.

Abstract

In this article, we are interested in endomorphism's impact on the commutativity of a Banach algebra. Our research uses a topological approach, drawing on specific results from functional analysis and algebraic techniques.\;Also, we provide examples to show that we need certain assumptions.